Claudio Meller found that
783742161 and all the numbers of the form
(7425)n741, for n=>0, have the following property:

R(n/3)-n=1....(*)

Example: 741 is such that 741/3= 247, & R(247)=742...

I tried to get solutions to this more general property:

Abs[R(n/3)-n]<=1.................(**)

I only got one more solution to (**), other than the already
reported by Meller, for n=42.

Q. Can you get other solutions to (**)?

Contributions came from Emmanuel Vantieghem

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Emmanuel wrote:

(7837421625)n 783742161 is a solution for (**). I could not find
others but the known ones.

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Wow!... this means that the "singular/isolated" solution reported by
Meller (783742161) is in fact the smallest solution of a set of infinite
solutions... As you can see the repeating part (7837421625) is a
kind of similar to the extreme/fixed part (783742161). This might have
been the clue to get this infinite family of solutions?... I will ask to
Emmanuel.(CR)

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This is the comment from Emmanuel to my question:

There is no secret behind the extra solutions I found for puzzle
615. I just 'tried' to reproduce the link between the solutions
742 and the numbers (7425)n 742. And it was successful (was it
the lucky of the dummies ?).